PhysicsLAB: Radiation of a Metal Cylinder

In this lab we are going to investigate the properties of an incandescent solid. We will be using a variety of specific heat specimens at room temperature as our incandescent solids. They will radiate in the IR part of the spectrum.

Each group will be given a metal cylinder composed of either lead, copper, aluminum, or zinc. Each metal has its own unique emissivity constant listed in the table below. These values are based on the conditions of our specimens and are not standard for every sample of that metal.

metal	emissivity
aluminum	0.4
lead	0.6
copper	0.8
zinc	0.3

In our analysis we will be using the following relationships for incandescent solids:

Wien's Law

Stefan-Boltzmann Law

e is the emissivity of the metal (0 <= e <= 1)

s is Stefan's constant which equals 5.67 ×10⁻⁸ W/(m² K⁴)

We will also be using the relationships:

wave speed

photon energy E = hf

where h is Planck's constant and equals 6.63 x 10^-34 Jsec

Since we are working with metal cylinders, you will also need to know how to calculate the surface area and volume of a cylinder

SA = 2prL + 2pr²

V = (pr²)L

The volume of a sphere is V = 4/3(pr³)

You will also need to remember how to calculate the mass density of a sample, r = M/V

Data Collection

Your metal sample is composed of what type of metal?

What is the mass of your cylinder in grams?

What is the height (length) of your cylinder in cm?

What is the diameter of your cylinder in cm?

What is the volume of your cylinder in cm³?

What is the density of your cylinder in g/cm³?

What is the total surface area of your cylinder in cm²?

What is its surface area in m²?

What is the room temperature in ºC?

What is the room temperature in Kelvin?

What is the emissivity of your cylinder's metal?

Data Analysis

Use the Stefan-Boltzmann Law to determine how much energy is radiated each second, power, by your cylinder (J/sec or watts).

Power = esAT⁴

Remember that all values must be in the MKS system. So your surface area must be in m² and your temperature must be in Kelvin.

Use Wien's Law to calculate the peak wavelength of your cylinder's radiation (m)

In which part of the electromagnetic spectrum does this wavelength belong?

infraredvisibleultraviolet

Using the fact that the speed of light is c = 3 x 10⁸ m/sec, determine the peak frequency of your cylinder's radiation in hz.

Determine the energy, in Joules, of a single photon emitted at the cylinder's peak frequency.

What is the total number of photons radiated each second by your cylinder?

Conclusions

In astronomy, the radiation energy density of a blackbody is given by the formula

u = aT⁴ where a = 7.5658 x 10^-16 J/m³/K⁴

This is a measure of the energy per unit volume emitted by a perfect blackbody based on its Kelvin temperature. This equation assumes that the photons carrying this energy are released isotropically (the same in all directions) and are traveling perpendicular to the emitting surface area. For our purpose, we can assume that we will let our generalized volume be spherical.

What would be the radiant energy density of a perfect blackbody in space if it were at the same temperature as your metal cylinder?

What is the volume of our perfect blackbody if it emits the same energy per second as our metal cylinder?

What would be the radius of our perfect blackbody radiator?

Which of Jupiter's moons has a comparable radius to our perfect blackbody radiator?